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Alloys possessing the shape memory effect are widely used in various fields of science, engineering, and medicine. For example, they are used in thermomechanical couplings of pipes. As distinct from conventional welded or soldered joints, such joints are characterized by good reliability and corrosion resistance, a high density of assembly, the possibility of connecting pipes of different materials and thicknesses, and absence of harmful thermal and electric effects. In Russian industry connecting sleeves are mainly produced from alloys based on titanium nickelides TNI and TNIK. Phase transformations occur in the region of positive temperatures in the TNI alloy and in the region of negative temperatures in the TNIK alloy. In order to determine whether the sleeves can be used repeatedly, we should know how repeated mandrelling (calibration of the openings) affects the temperature of phase transformations in titanium nickelides and the quality of the internal surfaces of these parts. These data cannot be found in the literature. The present work is devoted to this problem.The investigated sleeves were manufactured from rods of TNI (55% Ni, the remainder Ti) titanium nickelide 47 mm in diameter. According to data of the producer, the alloy has the following temperatures of initiation and completion of the forward martensite transformation: M i = 67°C, Mr= 54°C. For the backward martensite transformation A i =84°C, A r = 95oC.Cylindrical specimens 18 mm in diameter were cut along the axis of a rod by the electric-spark method. Then sleeves 18 mm long with an outer diameter of 16.5 mm were produced mechanically [I]. Four sealing belts 2 mm wide and 11.4 mm in diameter were mou~tcd on the internal surface of a sleeve [2].The sleeves were mandrelled at 22 _+ 2°C at a rate on I mm/min in a 1231U-10 testing machine. The outer diameter of the mandrel was 12.2 mm. On sleeves "charged" in this manner, we investigated the kinetics of the restoration of the initial shape (Fig. I). Inside sleeve 1 we placed mobile (2) and fixed (3) measuring elements with spring 4 between them, which provided continuous contact between the elements and the internal surface of the sleeve. The mobile element was structurally connected to armature 5, and the fixed element was connected to casing 6 of a capacitive deformation meter [3]. The temperature was measured by a thermocouple fastened to the surface of sleeve 1 by Teflon adhesive tape. The sleeve was heated at a rate of 5°C/rain by hot water Russian Federal Nuclear Center, All-Russia Research Institute for Experimental Physics. Arzarnas-16, Russia. poured into vessel 7. Two N-307/1 plotters recorded the temperature/time and deformation (constriction)/time dependences for three investigated sleeves. The error in measuring the deformation was _+ 20 p.m, and that in measuring the temperature was _+ 2°C. Results of the tests are presented in Table I. it can be seen that the degree of restoration of the diameter does not change considerably in repeated mandrelling, and the mandrelling force decr...